Independence Properties of Generalized Submodular Information Measures

Autor:	Asnani, Himanshu, Bilmes, Jeff, Iyer, Rishabh
Rok vydání:	2021
Předmět:	Computer Science - Information Theory Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	Recently a class of generalized information measures was defined on sets of items parametrized by submodular functions. In this paper, we propose and study various notions of independence between sets with respect to such information measures, and connections thereof. Since entropy can also be used to parametrize such measures, we derive interesting independence properties for the entropy of sets of random variables. We also study the notion of multi-set independence and its properties. Finally, we present optimization algorithms for obtaining a set that is independent of another given set, and also discuss the implications and applications of combinatorial independence. Comment: This paper was accepted at ISIT 2021. arXiv admin note: text overlap with arXiv:2006.15412
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2108.03154 Zobrazit plný text záznamu View this record from Arxiv